Any studio should provide a work for hire agreement on a demo without claiming any credit for writing. Any costs involved in providing a demo should be split equally between the parties involved in the cowrite.
Should a musicator charge time for him to record a demo?
If it involves using a studio and/or legitimate expenses he has to pay...yes. These expenses should be split equally with the cowriters.....it is up to the parties to agree in advance on what is to be done and who is to pay for it prior to any work taking place.
I see nothing wrong with a composer charging legit expenses for his studio services even if he is a cowriter. Most lyricists have no idea how much time and expense is involved in producing a demo......compared to just writing a lyric. As the song will have very little chance of making any money it is fair that this extra outlay to produce a demo be compensated.